P.S. I haven't done extensive testing on this, but you may be able to deploy Munki as a .pkg and not as a custom command that downloads the .pkg. You'll have to host it somewhere yourself (and Mosyle does not like the redirect URLs, so you'll legit have to host it), but you may want to try Management > Management Profiles > Install App > Add new profile. Then, under Installation source, pick Enterprise app, and then put in the URL of the hosted Munki installer .pkg.

To change the icon, just get a .png of whatever icon you want. Here's an example of how to generate that: